TWI739181B - A calibration method for a phased array antenna - Google Patents

Abstract

A calibration method for a phased array antenna, the phased array antenna comprising N antenna elements which are decomposed into G sub-arrays, each sub-array comprising M antenna elements, comprising the steps: (a) inputting a discrete Fourier transformation signal corresponding to an operation order r to the G sub-arrays; (b) measuring the far-field signals of the G sub-arrays corresponding to the operation order r; (c) repeating the steps a to b corresponding to the operation order from 1 to G for generating the calibration signal corresponding to the far-field signal of the G sub-array.

Description

Phase array antenna correction method

The present invention relates to a correction method of a phase array antenna, in particular to a correction method applied to a scanning beam phase array.

The radiation beam of the phased array antenna is generated by a beamforming network (BFN beamforming network), which includes active components and a phase shift converter to excite the antenna array. The frequency band of BFN applications has a trend of increasing, so BFN is easy to cause The phase error causes the beam defect, so that a complicated procedure is required to correct the phase array antenna.

In order to solve the above-mentioned problems, the present invention proposes an efficient correction method based on discrete Fourier transformation (DFT) to be applied to a phased array antenna.

The present invention proposes a phased array antenna applied to scanning beams, wherein the phased array antenna has N antenna elements, which is decomposed into G sub-arrays with M antenna elements, including the following steps: (a) Input the above G sub-arrays The discrete Fourier transform signals of the sub-arrays corresponding to the operation sequence r are in the G sub-arrays; (b) Measure the far-field signal corresponding to the operation sequence r of the above G sub-arrays at a fixed position; (c) Repeat the operation sequence r of steps (a) to (b) from 1 to G times to generate the corresponding G sub-arrays Far-field signal and G sub-array error correction signals.

More specifically, the phased array antenna is one-dimensional.

More specifically, the phased array antenna is two-dimensional.

More specifically, the phased array antenna correction method further includes the following steps: (d) input the discrete Fourier transform signals of the antenna elements corresponding to the M antenna elements of the G sub-arrays to the M antennas; (e) repeat Steps (a) to (d) measure M times to generate N antenna far-field signals and N antenna error correction signals.

More specifically, the phased array antenna correction method further includes the following steps: (f) inputting the amplitude signals corresponding to the above N antennas.

More specifically, in the step (f), the input amplitude signals A _p,g corresponding to the above N antennas, where p is M antenna numbers, 1 to M integers, g is G sub-array numbers, 1 to G integers .

，p為M個天線標號，1至M- 整數。 More specifically, the M antennas of the G sub-arrays in the step (b) correspond to the discrete Fourier transform signals of the antenna elements as

, P is the number of M antennas, 1 to M-integer.

。 More specifically, the discrete Fourier transform signals of the sub-array corresponding to the operation sequence r of the aforementioned G sub-arrays in the step (c) are exp(- i ( r -1)( g -1) Λ ), and g is the G sub-arrays The label, an integer from 1 to G, Λ is the phase difference between the above G sub-arrays, and

.

，p為M個天線標號，1至M-整數，g為G個子陣列標號，1至G整數。 More specifically, in the step (e), the G sub-array error correction signals are

, P is M antenna numbers, 1 to M-integer, g is G sub-array numbers, 1 to G integer.

，

，g表示子 陣列標號，p表示g子陣列中天線元素標號。 More specifically, in the step d, measuring the far-field signal corresponding to the operation sequence r of the N antennas at a fixed position is F _co ( q,r )=

,

, G represents the index of the sub-array, and p represents the index of the antenna element in the g sub-array.

[Figure 1] is a schematic flow chart of the phased array antenna calibration method of the present invention.

[Figure 2] is a schematic diagram of the scanning beam phased array antenna of the phased array antenna correction method of the present invention.

[Figure 3] is a schematic diagram of the phased array antenna decomposed into sub-array correction method of the phased array antenna correction method of the present invention.

[Figure 4] is a flow chart of the calibration method of the phased array antenna calibration method of the present invention.

[Figure 5] The comparison result of the amplitude and phase correction values of the one-dimensional phase array antenna correction method in the first embodiment of the phased array antenna correction method of the present invention and the preset values.

[Figure 6] is the comparison result of the radiation pattern before and after the calibration of the first embodiment of the phased array antenna calibration method of the present invention.

[Figure 7] is the comparison result of the amplitude and phase correction values of the one-dimensional phase array antenna correction method of the present invention in the second embodiment of the phase array antenna correction method and the preset values.

[Figure 8] is the comparison result of the radiation pattern before and after the calibration of the second embodiment of the phased array antenna calibration method of the present invention.

[Figure 9] The two-dimensional phased array antenna calibration method of the phased array antenna calibration method of the present invention is shown in the first The amplitude and phase correction values of the third embodiment are compared with the preset values.

[Figures 10(a) to 10(b)] are the comparison results of the influence of the error bounds of different bits of the DPS on the phase and amplitude errors of the phase array antenna correction method of the present invention.

[Figures 11(a) to 11(b)] are the results of the increase in the number of steps and the number of antenna elements in the phased array antenna correction method of the present invention on the accuracy.

[Figure 12] is a physical diagram of the digital phase shift translator and antenna array of the phase array antenna correction method of the present invention.

[Figure 13] The tracking amplitude and phase of the far-field measurement of the phased array antenna calibration method of the present invention.

[Figure 14] is a comparison diagram of the radiation pattern before and after the correction method of the phased array antenna of the present invention.

In order to further understand the technology, means and effects adopted by the present invention to achieve the predetermined purpose, please refer to the following detailed description and drawings of the present invention. The purpose, features, or characteristics of the present invention can be obtained from this in-depth and specific understanding, but the accompanying drawings are only provided for reference and explanation, and are not used to limit the present invention.

As shown in Figure 1, the steps of the calibration method of the present invention are: (a) input the discrete Fourier transform signals of the sub-arrays corresponding to the operation sequence r of the G sub-arrays to the G sub-arrays 101; (b) measure at a fixed position The aforementioned G sub-arrays correspond to the far-field signal 102 of the operation sequence r; (c) Repeat the operation sequence r of steps 101 to 102 from 1 to G times to generate the aforementioned G sub-array far-field signals and G sub-array error correction signals 103; (d) Input the discrete Fourier transform signals of the antenna elements corresponding to the M antenna elements of the G sub-arrays to the M antennas 104; (e) Repeat steps 101 to 104 to measure M times to generate N antenna far-field signals And N antenna error correction signals 102; (f) Input the amplitude signal 106 corresponding to the above N antennas.

As shown in Figure 2, the correction method of the present invention is applied to N phase array antennas that generate scanning beams, which are excited by active beam forming network 10 (beam forming network BFN) to radiate directional or circumferential beams ( directional/contoured beams), the active beam forming circuit includes a transmitter RF, a digital phase shifter PS (DPS digital phase shifter), an attenuator, a power splitter (not shown), and an antenna unit Ant.

其中I _n 為第n個天線元素的振幅，N為天線元素數，I _n 與φ _n 為第n個天線元素藉由功率器與相位移轉器101產生的振幅與相位，

(θ,

)為第n個天線元素的貢獻，而

(θ,

)為的公式為：

上述

為傳播方向的波向量，

為第n個天線元素位置向量，

(θ,

)為第n個天線元素的輻射場型，量測位置(θ,

)，量測遠場輻射場型為：

是共極化方向(co-polarization)的極化向量，I _n 併入通道不匹配引起的振幅誤差，φ _n =α _n +ω _n ，α _n 為通道不匹配引起的相位誤差，ω _n 為相位移轉器101產生的每個天線元素的相位。 The following first explains the correction principle of the one-dimensional (1-D) phased array antenna, the far-field radiation pattern is

Where I _n is the amplitude of the nth antenna element, N is the number of antenna elements, I _n and φ _n are the amplitude and phase of the nth antenna element generated by the power unit and the phase shifter 101,

( θ ,

) Is the contribution of the nth antenna element, and

( θ ,

) Is the formula:

Above

Is the wave vector in the direction of propagation,

Is the position vector of the nth antenna element,

( θ ,

) Is the radiation field pattern of the nth antenna element, and the measurement position (θ,

), the measured far-field radiation field type is:

Is the polarization vector in the co-polarization direction, I _{n is} incorporated into the amplitude error caused by channel mismatch, φ _n =α _n +ω _n , α _n is the phase error caused by channel mismatch, ω _n is The phase of each antenna element generated by the phase shifter 101.

其中

為併入激發振幅和天線元素輻射場型的振幅項，當 M=N，數位相位移轉器101連續切換時，(3)式中量測值F _co (m)和N個天線的振幅項A _n 形成離散傅立葉轉換關係式。 The digital phase shift converter 101 generates a digital phase shift converter with adjacent steps of △=2π/M by b-digit digital code, where M=2 ^b is the DPS step number, b is the phase shifter bit The digital phase can be expressed as ω _n,m = -2 π ( n -1)( m -1)/ M , the measured far-field radiation pattern is:

in

In order to incorporate the excitation amplitude and the amplitude terms of the antenna element radiation field pattern, when M=N and the digital phase shifter 101 continuously switches, the measured value F _co ( m ) in equation (3) and the amplitude terms of the N antennas A _n forms a discrete Fourier transform relationship.

，數位相位移轉器101在步階數 為M _γ 的情況下，以低位元數b-γ切換，藉由如此操作，量化誤差可以最小化，在陣列末端加入零元素(null element)以滿足DFT的關係式，其等效於施加DFT前的補零動作(zero padding)，然而當N>M時，其為常見大型相位陣列天線的狀況，是比較複雜的狀況，一種藉由分解相位陣列天線而無須關閉(shut down)其中天線元素的校正方法由此而生。 In general, the number of DPS steps M≠the number of antenna elements N, when N<M, the degradation coefficient is as follows:

When the number of steps is M _γ , the digital phase shifter 101 switches with the low bit number b-γ. By doing this, the quantization error can be minimized, and a null element is added at the end of the array to satisfy The relational expression of DFT is equivalent to zero padding before DFT is applied. However, when N>M, it is a common situation of large phased array antennas, which is a more complicated situation. The antenna does not need to be shut down (shut down) The correction method of the antenna element is born from this.

其中

As shown in Figure 3, it is a schematic diagram of the 1D phased array antenna correction method of the present invention. The phased array antenna has N antenna elements, which are decomposed into G sub-arrays. Each sub-array has M antenna elements. If necessary, finally A sub-array can be added with a null element. The calibration procedure requires a total of G operations, and each calibration procedure requires M measurement values. When the first operation (r=1), each sub-array is Its phase ω _p,g (subscript g represents the sub-array label, subscript p represents the antenna element label in the g sub-array) excites radiation to generate discrete Fourier transform terms, which are measured at a fixed position in the far field and add up each The discrete Fourier transform complex signal of the sub-arrays, when the second operation (r=2), each sub-array with its phase ω _p,g , plus the digital phase shift converter 101 to generate the corresponding phase shift (g-1 )Λ excitation, it is known from the linear nature of the discrete Fourier transform that at the rth operation, the following formula is obtained by measuring at a fixed position in the far field:

in

其中

By formula (4), the phase error of the p-th antenna element of each sub-array can be solved,

in

其中假設相位偏差δ _pq ~U[-δ _max ,δ _max ] 是平均分布在誤差界限δ _max ，因此當執行IDFT，第p追蹤值

值，也就是(8)式的逆離散傅立葉轉換，如(9)式所表示，

其中C _pq 為藉由IDFT所求解出之耦合係數。當δ _max 趨近於0時，並且p=q時，C _pq 趨近於1，而p≠q時，C _pq 趨近於0，這就化簡為理想DPS，然而當DPS量化誤差存在時，C _pq ≠0，每一個通道互相耦合，其他通道的貢獻無法省略，當子陣列天線元素數目增加時，其精確度會降低，

其中隨機變數X _pq 和Y _pq 並不是均勻分布而是反正弦分布，因此當DFT矩陣增加時誤差亦隨之累積，這就是為什麼退化係數(degeneration coefficient)在相位陣列天線元素數目N<M的校正中是必要的理由，然而，這並不是一個大問題，如果有大數目M的校正步階，相對應的RMS相位誤差通常是非常小，另一方面，當相位陣列天線元素數目N>M的校正中，分解相位陣列天線造成的誤差會隨著天線元素數目N增加而增加。 The accuracy and complexity of the calibration method proposed in this case depends on the calibration environment and the quantization error of the digital phase shifter 101. The error produced by the former is quite unpredictable. Therefore, it is a better calibration environment in a high-quality anechoic chamber, otherwise it will be required. The post-correction procedure reduces environmental spurious signals. The errors generated by the latter are the main purpose of the present invention. The quantization errors of the digital phase shifter 101 are often characterized as mean square (RMS) errors. These errors can be modeled as Perturbation of DFT,

It is assumed that the phase deviation δ _pq ~ U [-δ _max , δ _max ] is evenly distributed within the error limit δ _max , so when IDFT is performed, the p-th tracking value

Value, which is the inverse discrete Fourier transform of equation (8), as expressed in equation (9),

Where C _pq is the coupling coefficient obtained by IDFT. When δ _{m ax} approaches 0, and p=q, C _pq approaches 1, and when p≠q, C _pq approaches 0, which is simplified to ideal DPS, but when DPS quantization error exists When C _pq ≠ 0, each channel is coupled with each other, and the contribution of other channels cannot be omitted. When the number of sub-array antenna elements increases, its accuracy will decrease.

Among them, the random variables X _pq and Y _pq are not uniformly distributed but arc sine distribution, so when the DFT matrix increases, the error will also accumulate, which is why the degeneration coefficient is corrected for the number of phase array antenna elements N<M However, this is not a big problem. If there is a large number of M correction steps, the corresponding RMS phase error is usually very small. On the other hand, when the number of phased array antenna elements N>M In the calibration, the error caused by the decomposed phased array antenna will increase as the number of antenna elements N increases.

The complexity of the correction method of the present invention comes from the IDFT that decomposes the array antenna into sub-array measurement values and its (6) inverse matrix. In order to perform IDFT, the FFT algorithm can be used to reduce the order of complexity of its calculation. From the original complexity O( GM ^{2 d} ) to O( GM ^d log ₂ M ^d ), and the formula (6) is the Vandermonde matrix, when d=1, the array is one-dimensional (1-D), and d =2, the array is two-dimensional (2-D). When decomposing the array, the inverse matrix M needs to be solved, causing additional computational complexity to be O( G ² M ), and the matrix is also a Vandermonde matrix.

The calibration flowchart of the phased array antenna is shown in Figure 4. At first, the characteristics of the phased array antenna are used as the correction code, which includes the number of antenna elements N, the number of correction steps M of the digital phase shift converter 101, The radiation pattern of a single antenna element and other parameters, and then the calibration program will determine whether to perform the decomposition array or the degraded digital phase shift conversion based on the relationship between the number of antenna elements N and the number of steps M of the digital phase shift conversion. These are all corrections. The default value of the program. After the above-mentioned default value is completed, a selection table is generated to indicate the status of various measurement executions. When all the measurements are completed, the data has been collected, which is included in a single location Measure all phases and amplitudes, and get the excitation amplitude and phase of each array element. After correction, a new selection table is generated to provide an approximate digital phase shift zero state, which has been included in the phase error of each channel , Which is equivalent to the phase distribution of boresight radiation, and the newly generated selection table can be used to further optimize the radiation field.

Figure 5 is a comparison of the amplitude and phase correction values of the first embodiment of the one-dimensional phased array antenna correction method of the present invention with the preset values. In this embodiment, the one-dimensional phased array antenna includes 8 antenna elements and is equipped with 6 bits ( 64 states) DPS, the number of antenna elements N=8 is smaller than the number of states of DPS M=64 (or the number of steps), according to the Fig. 4 correction flow chart, perform degenerate DPS correction, the simulation results are shown in Figs. 5 and 6 As shown in the figure, figure 5 shows that the phase and amplitude correction calculation results are consistent with the preset values. After virtual correction, a new selection list is generated and the antenna elements are corrected to nearly equal phase. Figure 6 is the first embodiment Comparison of the radiation pattern before and after the correction, the phase error of the RF channel before the correction causes the phased array antenna to have a higher sidelobe level (SLL) and the main beam direction is slightly off the line of sight (boresight), but after correction Meet the ideal situation.

Figure 7 is a comparison of the amplitude and phase correction values of the second embodiment of the one-dimensional phased array antenna calibration method of the present invention with the preset values. Figure 8 is the comparison of the radiation pattern before and after the calibration of the second embodiment. This embodiment is The one-dimensional phased array antenna contains 12 antenna elements and is equipped with a 3-bit (8-state) DPS. The number of antenna elements N=12 is greater than the number of DPS states M=8 (or the number of steps). Correct the flow chart according to Figure 4. , Perform decomposition phase array antenna correction.

Figure 9 is the simulation result of phase amplitude in the third embodiment of the two-dimensional phased array antenna calibration method of the present invention. The two-dimensional phased array antenna includes 12x12 antenna elements and is equipped with a 3-bit (8-state) DPS.

The quantization error of DPS is very important to the accuracy of correction. Figure 10(a)(b) shows the influence of the error bounds of different bits of DPS on the phase and amplitude errors. The correction method is based on 64 antennas. Element one-dimensional phased array antenna configuration 3, 4, 5, 6, 7, 8 bit DPS test, each test is performed 10,000 times simulation, the average maximum amplitude error and phase error are calculated by calculating the correction value and the calculated value difference It can be observed that there is a linear trend. When the error bound of DPS decreases, the error of the correction result also decreases. When the error bound of DPS decreases close to zero, and under the condition of neglecting environmental correction factors, it is close to Ideal DPS, and the correction result error is also reduced to close to zero.

An interesting observation is that when the DPS error limit is fixed, the average amplitude and phase error of the array equipped with a 3-bit DPS is lower than that of the array equipped with a 4-bit DPS, so the trade-off between these parameters and accuracy must be paid attention to. .

As shown in Figure 10(a) and Figure 10(b), when the number of bits of DPS is higher than 6, the error curves almost overlap. Because of the degradation of DPS, M _γ =N=64. As shown in Table 1 below, when the error limit of DPS is δ _max = 5, the average amplitude and phase error of DPS with different parameters.

As shown in Figure 11(a) and Figure 11(b), respectively, the effect of increasing the number of steps and the number of antenna elements on the accuracy is shown. These results are obtained by averaging after 10,000 simulations. In Figure 11(a) Under the condition that the number of DPS bits is fixed at 3 bits and the error limit δ _max = 5, the number of antenna elements changes from 8 to 64. It can be seen from the simulation results that the error limit of the correction increases with the increase of the number of antenna elements. In Figure 10(b), when the number of fixed groups is 1, and =M, the number of bits in DPS varies from 2 to 12. Contrary to the previous situation, there is a linear relationship between the error and the number of bits.

Figure 12 is the physical diagram of the digital phase shifter and antenna array.

Figure 13 shows the tracking amplitude and phase of the far-field measurement.

Figure 14 is a comparison diagram of the radiation pattern before and after correction.

The advantages of the phased array antenna calibration method provided by the present invention when compared with other conventional technologies are as follows:

(1) The present invention is especially used when the output phase of the phase shift converter is digitized to provide the same phase step size, and the far-field radiation data and the excitation data of the antenna elements satisfy the Fourier transform relationship, so DFT It can be used to calibrate the antenna array so that the co-polarization far-field radiation source has an equal phase in the boresight direction, so that the digital phase shifter stores the error correction phase as a reference value for scanning the beam.

(2) The advantage of the present invention is that the processing speed of electronic beam scanning is much faster than that of mechanical probe scanning.

(3) The purpose of the present invention is to propose a phased array antenna applied to scanning beams, which can correct multiple antennas at the same time through the FFT algorithm decomposed into sub-arrays, and reduce the complexity of calculating the phase error.

The present invention has been disclosed above through the above-mentioned embodiments, but it is not intended to limit the present invention. Anyone familiar with this technical field with ordinary knowledge should understand the aforementioned technical features and embodiments of the present invention without departing from the scope of the present invention. Within the spirit and scope, no changes and modifications can be made. Therefore, the scope of patent protection of the present invention shall be subject to the definition of the claims attached to this specification.

Claims (9)

A phased array antenna correction method, wherein the above-mentioned phased array antenna has N antenna elements, which are decomposed into G sub-arrays with M antenna elements, and the phased array antenna correction method includes the following steps: (a) Input the above G sub-arrays The discrete Fourier transform signals of the sub-arrays corresponding to the operation sequence r are in the G sub-arrays; (b) measure the far-field signals of the G sub-arrays corresponding to the operation sequence r at a fixed position; (c) repeat steps (a) to (b) ) The operation sequence r is from 1 to G times to generate the far-field signals corresponding to the G sub-arrays and the G sub-array error correction signals; (d) Input the discrete Fourier transform signals corresponding to the antenna elements of the M antenna elements of the G sub-arrays In the above M antennas; and (e) repeat steps (a) to (d) to measure M times to generate N antenna far-field signals and N antenna error correction signals. The phased array antenna correction method according to claim 1, wherein the phased array antenna is one-dimensional. The phased array antenna correction method according to claim 1, wherein the phased array antenna is two-dimensional. The phased array antenna calibration method as described in claim 1, further comprising the following steps: (f) Input the amplitude signals corresponding to the above N antennas. The phased array antenna calibration method according to the item request, wherein step (f) the antenna corresponding to the N input amplitude signal A _{p, g, p} antenna number is M, an integer of 1 to M, g is a sub-G Array label, integer from 1 to G. The phased array antenna correction method according to claim 1, wherein the M antennas of the G sub-arrays in step (b) correspond to the discrete Fourier transform signals of the antenna elements:

1)), p is the number of M antennas, an integer from 1 to M. The phased array antenna correction method according to claim 1, wherein the discrete Fourier transform signals of the sub-array corresponding to the operation sequence r of the G sub-arrays in step (c) are exp(- i ( r -1)( g -1) Λ ), g is the number of G sub-arrays, integers from 1 to G, Λ is the phase difference between the above G sub-arrays, and

, △=2π/M. The phased array antenna correction method according to claim 1, wherein the G sub-array error correction signals in step e are

, P is M antenna numbers, 1 to M integers, g is G sub-array numbers, 1 to G integers. The phased array antenna calibration method according to claim 1, wherein the far-field signal of the operation sequence r corresponding to the above N antennas measured at a fixed position in step d is F _co ( q,r )=

,

, G represents the index of the sub-array, and p represents the index of the antenna element in the g sub-array.

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